Kabul, Afghanistan (CNN) -- The top U.S. general in Afghanistan vowed that coalition forces "are absolutely going to secure Kandahar," as security efforts expand in the country's south.

"We already are doing a lot of security operations in Kandahar, but it's our intent -- under President [Hamid] Karzai -- to make an even greater effort there," Gen. Stanley McChrystal told a joint news conference Monday with Mark Sedwill, the NATO senior civilian representative to the country.

The news conference coincided with a visit by U.S. Secretary of Defense Robert Gates, who was also to meet with Karzai.

McChrystal indicated a military operation could begin in the volatile Kandahar province as early as this summer, but both Sedwill and McChrystal cautioned that much political groundwork lay ahead for NATO-led coalition troops before an offensive can begin. Just as in the recent Marjah operation, the goal, they said, is to gain the support of the Afghan people.

"What I think we've learned about operations in Afghanistan ... is if you try to push against the culture, you have huge problems," McChrystal said. "What we're trying to achieve in Kandahar is to do the political groundwork so when it's time to do the military operation, the significant part of the population is pulling us in and supportive so we're not only doing what they want but we're operating in a way that they're comfortable with. That's the key to success here."

McChrystal said the goal "is to demonstrate again that we can operate in a way where we've got strong resolve by the government of Afghanistan, effective performance by the Afghan military and coalition partners, and government partners, so that as we do an operation that shows the people of Kandahar, and the Taliban as well, that operations like this actually result in a better outcome for everyone."

He declined to comment specifically on when the Kandahar offensive will begin, but said "our forces will be significantly increased around there by early summer."

"There won't be a 'D-Day' that is climactic," McChrystal said. "It will be a rising tide of security as it comes."

The push to secure Kandahar from what McChrystal calls a "menacing Taliban presence" is part of a larger counterinsurgency effort in the country's south, started last month in Marjah in southern Helmand province.

Long a bastion of pro-Taliban sentiment and awash with the opium used to fund the insurgency, the Marjah region has been known as the heroin breadbasket of Afghanistan and as a place where the Taliban had set up a shadow government.

The hope now is for the United States to persuade the locals to change their crops from poppies -- grown to produce opium for the Taliban's drug trade -- and instead grow crops such as wheat, which can help them survive and provide income as well.

Sedwill and McChrystal praised the early stages of the Marjah offensive, with Sedwill calling it a "template for the way we want to take this campaign forward over the next year to 18 months."

McChrystal said that in addition to the strategic importance of the Marjah offensive, the operation was a "demonstration to the Afghan people, to the international community, to the Pakistanis, and very important to the Taliban as well, that things have changed."